# Statistics 3022

1816 Words Apr 23rd, 2011 8 Pages
1. Following the explosion of the 25th space shuttle ﬂight, which was caused by an O-ring failure in one or more of the booster rockets, data from the previous 24 ﬂights were studied. The Temperature (F) at the time of launch and whether or not there was evidence of O-ring failures for each of the previous 24 shuttle ﬂights was determined for each ﬂight. A logistic regression relating the Failure of O-rings to the Temperature was obtained with the following result:

Estimate Std. Error z value Intercept 15.2954317 7.3280842 2.088 Temperature -0.2360002 0.1073615 2.198 a. What is the ﬁtted logistic regression equation for predicting the log(odds) of an O-ring failure?

b. If the temperature at launch was 63 F, what are the estimated odds of
The data are given in the table below: 1 2 3 4 5 Subject Beginning cholesterol 275 255 283 261 263 Cholesterol after 6 months 264 262 260 252 259 11 −7 23 9 4 Diﬀerence a. What should the researchers establish as the appropriate alternative hypothesis?

b. The ﬁve diﬀerences are to be assigned an appropriate rank. What rank should the diﬀerence of 7 be assigned?

c. Under the null hypothesis that the responses have a continuous distribution that is not aﬀected by the treatment, what is the expected value of the test statistic W+?

d. What is the observed value of W+?

e. Test the relevant hypotheses at 5% level of signiﬁcance.

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5. According to an article in a recently published medical journal, one-third of all sets of triplets consist of all females, one-fourth of all males, and the remaining sets of triplets are of mixed gender. A simple random sample of 78 sets of triplets born in the past 20 years is obtained from hospital records. The results are presented below: All female All male Mixed gender Total 10 11 57 78 Based on the above data, is the claim made in the medical journal true?

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6. We wish to see if the dial indicating the oven temperature for a certain model oven is properly calibrated. Four ovens of this model are selected at random. The dial on each is set to 300F, and after one